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anonymous

  • one year ago

Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <7, 2>, v = <21, 6>

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  1. jim_thompson5910
    • one year ago
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    let u and v be two vectors they are orthogonal if and only if u dot v = 0 ------------------------------------------------------- they are parallel if and only if v = k*u where k is some scalar

  2. anonymous
    • one year ago
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    ok so how do i find u dot v

  3. jim_thompson5910
    • one year ago
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    u = <a,b> v = <c,d> u dot v = a*c + b*d the * means multiplication between two scalars u,v are vectors a,b,c,d are scalars

  4. jim_thompson5910
    • one year ago
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    example u = <2,3> v = <7,9> u dot v = 2*7 + 3*9 = 14 + 27 = 41

  5. jim_thompson5910
    • one year ago
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    "dot" refers to the dot product of two vectors

  6. anonymous
    • one year ago
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    Ok so for my problem u dot v = 159.

  7. jim_thompson5910
    • one year ago
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    correct

  8. jim_thompson5910
    • one year ago
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    since that result isn't 0, the vectors aren't orthogonal

  9. anonymous
    • one year ago
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    How would I determine if they are parallel or not?

  10. jim_thompson5910
    • one year ago
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    can you find some scalar k that makes v = k*u true?

  11. jim_thompson5910
    • one year ago
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    does k = 5 make v = k*u true? ie is v = 5*u true?

  12. jim_thompson5910
    • one year ago
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    Alternate method Let u = <a,b> v = <c,d> u and v are parallel if and only if a/c = b/d is true

  13. anonymous
    • one year ago
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    Okay I got 7/ 21 = 2/6 so they are parallel, thanks!

  14. jim_thompson5910
    • one year ago
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    yep they are parallel

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